Study on Revolving Gravity Waves in Liquid-Elastic Shells Coupled System
|Keywords||nonlinear vibration liquid-elastic shells coupled system revolving gravity waves coupled resonance singularity theory|
In the recent years, nonlinear science is the important research project in domestic and international academic. As far as the liquid-solid coupled system which lies in engineering structure widely, the nonlinear factor in the system is not be ignored. It is of great value to study the nonlinear vibration of the liquid-solid coupled system.The nonlinear vibration of the liquid-elastic shell coupled system is studied in the paper;the free surface motion and the elastic shell displacement are considered. Analyze the vibration of the liquid-elastic shell coupled system subjected to the high-frequency excitation with the revolving gravity waves appearing. The phenomenon of the revolving gravity waves is discussed from the aspect of the vibration mechanism、 the dynamical character、 the change of the system parameter, and so on. The concrete work is showed in the following text.1. Based on the experimental phenomenon that the low-frequency and large-amplitude traveling gravity waves may be generated by the high-frequency external excitation in the liquid-elastic shell coupled system, according as the boundary conditions at the fluid-structure interface, a set of nonlinear equations for the multi-degree of freedom system is constructed with the use of the knowledge of hydromechanics and elasticity.2. The numerical computation is carried out by means of the Runge-Kutta method. The time history curves and frequency spectrum curves are obtained, and amplitude-frequency characteristic curves are obtained by changing the amplitude and frequency of the exciting force. Sequentially analyze the dynamical character of the liquid-elastic shell coupled system.3. The theoretical analysis is carried out by the means of averaging method. A set of nonlinear differential equations for the four-degree of freedom system is solved. According to the steady state solution of the first order approximation obtained, the relationship between the amplitude and the frequency of the external excitation and the response of the revolvinggravity waves is established, which makes the vibration mechanism more clear. The results show good agreement with the numerical results. 4. The frequency and the amplitude of the excitation are considered to be the bifurcation parameter respectively. The bifurcation behaviors are discussed according to singularity theory, and many bifurcation models and transition sets are also obtained. The relationship between the system parameter and the bifurcation behavior is constituted, which supplies the theoretical reference for the analysis of the system.On the basis of the numerical computation and the theoretical analysis, an in-depth study is given to explain the vibration mechanism of the low-frequency and high-amplitude revolving gravity wave in the liquid-elastic shell coupled system. The results agree generally with the experimental results.